Simplify the following expression: $p = \dfrac{-6n^2 - 66n - 108}{n + 2} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ p =\dfrac{-6(n^2 + 11n + 18)}{n + 2} $ Then we factor the remaining polynomial: $n^2 + {11}n + {18} $ ${2} + {9} = {11}$ ${2} \times {9} = {18}$ $ (n + {2}) (n + {9}) $ This gives us a factored expression: $\dfrac{-6(n + {2}) (n + {9})}{n + 2}$ We can divide the numerator and denominator by $(n - 2)$ on condition that $n \neq -2$ Therefore $p = -6(n + 9); n \neq -2$